## Hidden Valley Processes

This Hidden Valley (HV) scenario has been developed specifically to allow the study of visible consequences of radiation in a hidden sector, by recoil effect. A key aspect is therefore that the normal timelike showering machinery has been expanded with a third kind of radiation, in addition to the QCD and QED ones. These three kinds of radiation are fully interleaved, i.e. evolution occurs in a common pT-ordered sequence. The scenario is described in [Car10]. Furthermore hadronization in the hidden sector has been implemented. Three main scenarios for production into and decay out of the hidden sector can be compared, in each case either for an Abelian or a non-Abelian gauge group in the HV. For further details see [Car11].
Warning: do not use the alternative hadronization scenarios `StringPT:thermalModel = on` or `StringPT:mT2suppression = on` in conjunction with Hidden Valley processes, since they have not been constructed to work together.

### Particle content and properties

For simplicity we assume that the HV contains an unbroken SU(N) gauge symmetry. This is used in the calculation of production cross sections. These could be rescaled by hand for other gauge groups.

`mode` HiddenValley:Ngauge (`default = 3`; `minimum = 1`)
is U(1) for `Ngauge = 1`, is SU(N) if `Ngauge > 1`. Note that pair production cross sections contains a factor of `Ngauge` for new particles in the fundamental representation of this group.

A minimal HV particle content has been introduced. Firstly, there is a set of 12 particles that mirrors the Standard Model flavour structure, and is charged under both the SM and the HV symmetry groups. Each new particle couples flavour-diagonally to a corresponding SM state, and has the same SM charge and colour, but in addition is in the fundamental representation of the HV colour, as follows:
`Dv`, identity 4900001, partner to the normal `d` quark;
`Uv`, identity 4900002, partner to the normal `u` quark;
`Sv`, identity 4900003, partner to the normal `s` quark;
`Cv`, identity 4900004, partner to the normal `c` quark;
`Bv`, identity 4900005, partner to the normal `b` quark;
`Tv`, identity 4900006, partner to the normal `t` quark;
`Ev`, identity 4900011, partner to the normal `e` lepton;
`nuEv`, identity 4900012, partner to the normal `nue` neutrino;
`MUv`, identity 4900013, partner to the normal `mu` lepton;
`nuMUv`, identity 4900014, partner to the normal `numu` neutrino;
`TAUv`, identity 4900015, partner to the normal `tau` lepton;
`nuTAUv`, identity 4900016, partner to the normal `nutau` neutrino.
Collectively we will refer to these states as `Fv`; note, however, that they need not be fermions themselves.

In addition the model contains the HV gauge particle, either a HV-gluon or a HV-photon, but not both; see `Ngauge` above:
`gv`, identity 4900021, is the massless gauge boson of the HV SU(N) group;
`gammav`, identity 4900022, is the massless gauge boson of the HV U(1) group.

Finally, for the basic HV scenario, there is a new massive particle with only HV charge sitting in the fundamental representation of the HV gauge group:
`qv`, identity 4900101.

The typical scenario would be for pair production of one of the states presented first above, e.g. g g → Dv Dvbar. Such a Dv can radiate gluons and photons like an SM quark, but in addition HV-gluons or HV-photons in a similar fashion. Eventually the Dv will decay like Dv → d + qv. The strength of this decay is not set as such, but is implicit in your choice of width for the Dv state. Thereafter the d and qv can radiate further within their respective sectors. The qv, gv or gammav are invisible, so their fate need not be considered further.

While not part of the standard scenario, as an alternative there is also a kind of Z' resonance:
`Zv`, identity 4900023, a boson that can couple both to pairs of Standard Model fermions and to qv qvbar pairs. Mass, total width and branching ratios can be set as convenient.
This opens up for alternative processes l^+l^-, q qbar → Zv → qv qvbar.

The possibility of a leakage back from the hidden sector will be considered in the Hadronization section below. For the U(1) case the gammav acquires a mass and can decay back to a Standard-Model fermion pair, while the qv remains invisible. The SU(N) alternative remains unbroken, so confinement holds and the gv is massless. A string like qv - gv - ... - gv - qvbar can break by the production of new qv - qvbar pairs, which will produce qv-qvbar mesons. It would be possible to build a rather sophisticated hidden sector by trivial extensions of the HV flavour content. For now, however, the qv can be duplicated in up to eight copies with the same properties except for the flavour charge. These are assigned codes 4900101 - 4900108. This gives a total of 64 possible lowest-lying mesons. We also include a duplication of that, into two multiplets, corresponding to the pseudoscalar and vector mesons of QCD. For now, again, these are assumed to have the same mass and other properties. By default, only the flavour-diagonal ones can decay back into the Standard-Model sector, however, while the rest remains in the hidden sector. It is therefore only necessary to distinguish a few states:
`pivDiag`, identity 4900111, a flavour-diagonal HV-meson with spin 0 that can decay back into the Standard-Model sector;
`rhovDiag`, identity 4900113, a flavour-diagonal HV-meson with spin 1 that can decay back into the Standard-Model sector;
`pivUp`, identity 4900211, an off-diagonal HV-meson with spin 0 that is stable and invisible, with an antiparticle `pivDn` with identity -4900211; the particle is the one where the code of the flavour is larger than that of the antiflavour;
`rhovUp`, identity 4900213, an off-diagonal HV-meson with spin 1 that is stable and invisible, with an antiparticle `rhovDn` with identity -4900213; again the particle is the one where the code of the flavour is larger than that of the antiflavour;
`ggv`, identity 4900991, is only rarely used, to handle cases where it is kinematically impossible to produce an HV-meson on shell, and it therefore is assumed to de-excite by the emission of invisible gv-gv v-glueball bound states.

By changing ParticleData, it is possible to allow decays even for the off-diagonal Up/Dn mesons.

Only the spin of the HV-gluon or HV-photon is determined unambiguously to be unity, for the others you can make your choice.

`mode` HiddenValley:spinFv (`default = 1`; `minimum = 0`; `maximum = 2`)
The spin of the HV partners of the SM fermions, e.g. Dv, Uv, Ev and nuEv.
`option` 0 : spin 0.
`option` 1 : spin 1/2.
`option` 2 : spin 1.

`mode` HiddenValley:spinqv (`default = 0`; `minimum = 0`; `maximum = 1`)
The spin of qv when the Fv (the HV partners of the SM fermions) have spin 1/2. (While, if they have spin 0 or 1, the qv spin is fixed at 1/2.)
`option` 0 : spin 0.
`option` 1 : spin 1.

`parm` HiddenValley:kappa (`default = 1.`)
If the Fv have spin 1 then their production cross section depends on the presence of anomalous magnetic dipole moment, i.e. of a kappa different from unity. For other spins this parameter is not used.

`flag` HiddenValley:doKinMix (`default = off`)
allow kinematic mixing or not.

`parm` HiddenValley:kinMix (`default = 1.`)
strength of kinetic mixing.

You should set the Fv and qv masses appropriately, with the latter smaller than the former two to allow decays. When U(1) hadronization is switched on, you need to set the gammav mass and decay modes. For SU(N) hadronization the HV-meson masses should be set to match the qv ones. The simplest is to assume that m_qv defines a constituent mass, so that m_HVmeson = 2 m_qv. The hvMesonDiag decay modes also need to be set.

### Production processes

`flag` HiddenValley:all (`default = off`)
Common switch for the group of all hard Hidden Valley processes, as listed separately in the following.

`flag` HiddenValley:gg2DvDvbar (`default = off`)
Pair production g g → Dv Dvbar. Code 4901.

`flag` HiddenValley:gg2UvUvbar (`default = off`)
Pair production g g → Uv Uvbar. Code 4902.

`flag` HiddenValley:gg2SvSvbar (`default = off`)
Pair production g g → Sv Svbar. Code 4903.

`flag` HiddenValley:gg2CvCvbar (`default = off`)
Pair production g g → Cv Cvbar. Code 4904.

`flag` HiddenValley:gg2BvBvbar (`default = off`)
Pair production g g → Bv Bvbar. Code 4905.

`flag` HiddenValley:gg2TvTvbar (`default = off`)
Pair production g g → Tv Tvbar. Code 4906.

`flag` HiddenValley:qqbar2DvDvbar (`default = off`)
Pair production q qbar → Dv Dvbar via intermediate gluon. Code 4911.

`flag` HiddenValley:qqbar2UvUvbar (`default = off`)
Pair production q qbar → Uv Uvbar via intermediate gluon. Code 4912.

`flag` HiddenValley:qqbar2SvSvbar (`default = off`)
Pair production q qbar → Sv Svbar via intermediate gluon. Code 4913.

`flag` HiddenValley:qqbar2CvCvbar (`default = off`)
Pair production q qbar → Cv Cvbar via intermediate gluon. Code 4914.

`flag` HiddenValley:qqbar2BvBvbar (`default = off`)
Pair production q qbar → Bv Bvbar via intermediate gluon. Code 4915.

`flag` HiddenValley:qqbar2TvTvbar (`default = off`)
Pair production q qbar → Tv Tvbar via intermediate gluon. Code 4916.

`flag` HiddenValley:ffbar2DvDvbar (`default = off`)
Pair production f fbar → Dv Dvbar via intermediate gamma*/Z^*. Code 4921.

`flag` HiddenValley:ffbar2UvUvbar (`default = off`)
Pair production f fbar → Uv Uvbar via intermediate gamma*/Z^*. Code 4922.

`flag` HiddenValley:ffbar2SvSvbar (`default = off`)
Pair production f fbar → Sv Svbar via intermediate gamma*/Z^*. Code 4923.

`flag` HiddenValley:ffbar2CvCvbar (`default = off`)
Pair production f fbar → Cv Cvbar via intermediate gamma*/Z^*. Code 4924.

`flag` HiddenValley:ffbar2BvBvbar (`default = off`)
Pair production f fbar → Bv Bvbar via intermediate gamma*/Z^*. Code 4925.

`flag` HiddenValley:ffbar2TvTvbar (`default = off`)
Pair production f fbar → Tv Tvbar via intermediate gamma*/Z^*. Code 4926.

`flag` HiddenValley:ffbar2EvEvbar (`default = off`)
Pair production f fbar → Ev Evbar via intermediate gamma*/Z^*. Code 4931.

`flag` HiddenValley:ffbar2nuEvnuEvbar (`default = off`)
Pair production f fbar → nuEv nuEvbar via intermediate gamma*/Z^*. Code 4932.

`flag` HiddenValley:ffbar2MUvMUvbar (`default = off`)
Pair production f fbar → MUv MUvbar via intermediate gamma*/Z^*. Code 4933.

`flag` HiddenValley:ffbar2nuMUvnuMUvbar (`default = off`)
Pair production f fbar → nuMUv nuMUvbar via intermediate gamma*/Z^*. Code 4934.

`flag` HiddenValley:ffbar2TAUvTAUvbar (`default = off`)
Pair production f fbar → TAUv TAUvbar via intermediate gamma*/Z^*. Code 4935.

`flag` HiddenValley:ffbar2nuTAUvnuTAUvbar (`default = off`)
Pair production f fbar → nuTAUv nuTAUvbar via intermediate gamma*/Z^*. Code 4936.

`flag` HiddenValley:ffbar2Zv (`default = off`)
Production f fbar → Zv where Zv is a generic resonance that couples both SM fermion pairs and a qv qvbar pair. Not part of the framework of the above processes, but as an alternative. Code 4941.

### Timelike showers

One key point of this HV scenario is that radiation off the HV-charged particles is allowed. This is done by the standard final-state showering machinery. (HV particles are not produced in initial-state radiation.) All the (anti)particles Fv and qv have one (negative) unit of HV charge. That is, radiation closely mimics the one in QCD. Both QCD, QED and HV radiation are interleaved in one common sequence of decreasing emission pT scales. Each radiation kind defines a set of dipoles, usually spanned between a radiating parton and its recoil partner, such that the invariant mass of the pair is not changed when a radiation occurs. This need not follow from trivial colour assignments, but is often obvious. For instance, in a decay Qv → q + qv the QCD dipole is between the q and the hole after Qv, but qv becomes the recoiler should a radiation occur, while the role of q and qv is reversed for HV radiation.

This also includes matrix-element corrections for a number of decay processes, with colour, spin and mass effects included [Nor01]. They were calculated within the context of the particle content of the MSSM, however, which does not include spin 1 particles with unit colour charge. In such cases spin 0 is assumed instead. By experience, the main effects come from mass and colour flow anyway, so this is not a bad approximation. (Furthermore the MSSM formulae allow for gamma_5 factors from wave functions or vertices; these are even less important.)

An emitted gv can branch in its turn, gv → gv + gv. This radiation may affect momenta in the visible sector by recoil effect, but this is a minor effect relative to the primary emission of the gv.

While the default model has a fixed Hidden Valley coupling alpha_HV, some further work [Scw15] has considered the impact of a running coupling. This is included as an option.

`flag` HiddenValley:FSR (`default = off`)
switch on final-state shower of gv or gammav in a HV production process.

`mode` HiddenValley:alphaOrder (`default = 0`; `minimum = 0`; `maximum = 1`)
Order at which alpha_HV runs,
`option` 0 : zeroth order, i.e. alpha_HV is kept fixed at the value alphaFSR.
`option` 1 : first order, with the beta function based on Ngauge and Nflav.

`parm` HiddenValley:alphaFSR (`default = 0.1`; `minimum = 0.0`)
fixed alpha scale of gv/gammav emission; corresponds to alpha_strong of QCD or alpha_em of QED. For shower branchings such as Dv → Dv + gv the coupling is multiplied by C_F = (N^2 - 1) / (2 * N) for an SU(N) group and for gv → gv + gv by N.

`parm` HiddenValley:Lambda (`default = 0.4`; `minimum = 0.1`)
the parameter used for the case of a running (first order) alpha_HV.

`parm` HiddenValley:pTminFSR (`default = 0.44`; `minimum = 0.1`)
lowest allowed pT of emission. Should be greater than or equal to 1.1 times Lambda, or it will be reset automatically.

### Hadronization

By default the HV particles with no Standard Model couplings are not visible. Their presence can only be deduced by the observation of missing (transverse) momentum in the event as a whole. In the current implementation it is possible to simulate two different scenarios where activity can leak back from the hidden sector.

The first possibility is relevant for the U(1) scenario. The U(1) group may be broken, so that the gammav acquires a mass. Furthermore, the gammav may have a small mixing angle with the normal photon, or with some Z' state or other mediator, and may thus decay back into Standard Model particles. The qv still escapes undetected; recall that there is no confinement in the U(1) option.

In order to enable this machinery two commands are necessary, `4900022:m0 = ...` to set the gammav mass to the desired value, and `4900022:onMode = on` to enable gammav decays. The default gammav decay table contains all Standard Model fermion-antifermion pairs, except top, with branching ratios in proportion to their coupling to the photon, whenever the production channel is allowed by kinematics. This table could easily be tailored to more specific models and needs. For instance, for a mass below 1 - 2 GeV, it would make sense to construct a table of exclusive hadronic decay channels rather than go the way via a hadronizing quark pair.

The gammav are expected to decay so rapidly that no secondary vertex will be detectable. However, it is possible to set `4900022:tau0` to a finite lifetime (in mm) that will be used to create separated secondary vertices.

The second, more interesting, possibility is relevant for the SU(N) scenarios. Here the gauge group remains unbroken, i.e. gv is massless, and the partons are confined. Like in QCD, the HV-partons can therefore be arranged in one single HV-colour-ordered chain, with a qv in one end, a qvbar in the other, and a varying number of gv in between. Each event will only contain (at most) one such string, (i) since perturbative branchings gv → qv qvbar have been neglected, as is a reasonable approximation for QCD, and (ii) since HV-colours are assigned in the N_C → infinity limit, just like in the handling of string fragmentation in QCD. The HV-string can then fragment by the nonperturbative creation of qv qvbar pairs, leading to the formation of HV-mesons along the string, each with its qv from one vertex and its qvbar from the neighbouring one.

Since, so far, we have only assumed there to be one qv species, all produced qv qvbar HV-mesons are of the same flavour-diagonal species. Such an HV-meson can decay back to the normal sector, typically by whatever mediator particle allowed production in the first place. In this framework the full energy put into the HV sector will leak back to the normal one. To allow more flexibility, an ad hoc possibility of n_Flav different qv species is introduced. For now they are all assumed to have the same mass and other properties, but distinguished by some flavour-like property. Only the flavour-diagonal ones can decay, meaning that only a fraction (approximately) 1/n_Flav of the HV-energy leaks back, while the rest remains in the hidden sector.

This scenario contains more parameters than the first one, for the U(1) group. They can be subdivided into two sets. One is related to particle properties, both for qv and for the two different kinds of HV-mesons, here labeled 4900111 and 4900113 for the diagonal ones, and +-4900211 and +-4900213 for the off-diagonal ones. It makes sense to set the HV-meson masses to be twice the qv one, as in a simple constituent mass context. Furthermore the hvMesonDiag decay modes need to be set up. Like with the gammav in the U(1) option, the default decay table is based on the branching ratios of an off-shell photon.

The second set are fragmentation parameters that extend or replace the ones used in normal string fragmentation. Some of them are not encoded in the same way as normally, however, but rather scale as the qv mass is changed, so as to keep a sensible default behaviour. This does not mean that deviations from this set should not be explored, or that other scaling rules could be preferred within alternative scenarios. These parameters are as follows.

`flag` HiddenValley:fragment (`default = off`)
switch on string fragmentation of the HV partonic system. Only relevant for SU(N) scenarios.

`mode` HiddenValley:nFlav (`default = 1`; `minimum = 1`; `maximum = 8`)
number of different flavours assumed to exist in the hadronization description, leading to approximately 1/n_Flav of the produced HV-mesons being flavour-diagonal and capable to decay back to Standard Model particles.

`parm` HiddenValley:probVector (`default = 0.75`; `minimum = 0.`; `maximum = 1.`)
fraction of HV-mesons that are assigned spin 1 (vector), with the remainder spin 0 (pseudoscalar). Assuming the qv have spin 1/2 and the mass splitting is small, spin counting predicts that 3/4 of the mesons should have spin 1.

`parm` HiddenValley:aLund (`default = 0.3`; `minimum = 0.0`; `maximum = 2.0`)
The a parameter of the Lund symmetric fragmentation function. See the normal fragmentation function description for the shape of this function.

`parm` HiddenValley:bmqv2 (`default = 0.8`; `minimum = 0.2`; `maximum = 2.0`)
The b parameter of the Lund symmetric fragmentation function, multiplied by the square of the qv mass. This scaling ensures that the fragmentation function keeps the same shape when the qv mass is changed (neglecting transverse momenta).

`parm` HiddenValley:rFactqv (`default = 1.0`; `minimum = 0.0`; `maximum = 2.0`)
r_qv, i.e. the Bowler correction factor to the Lund symmetric fragmentation function, which could be made weaker or stronger than its natural value.

`parm` HiddenValley:sigmamqv (`default = 0.5`; `minimum = 0.0`)
the width sigma of transverse momenta in the HV fragmentation process, normalized to the qv mass. This ensures that sigma scales proportionately to m_qv. See the normal fragmentation pT description for conventions for factors of 2.